CYCLIC DECOMPOSITIONS OF COMPLETE GRAPHS INTO K_(k,m) + e : THE MISSING CASE

摘要

We prove that the complete graph K_n with n = 2(km+1)x + l vertices can be cyclically decomposed into K_(k,m) + e, the graph arising from the complete bipartite graph K_(k,m), k,m ≥ 2 by adding one edge into the partite set of order k. This result complements a previous result by S. I. El-Zanati, W. A. O'Hanlon, and E. R. Spicer, who used different construction to prove it for k > 2.